maria and tim sold candy bars for a fundraiser.maria sold 7 less than twice the number of candy bars that tim sold.in total maria and tim sold 137 candy bars.find the amount of candy bars sold by each
bars sold by Tim ---- x
Maria ----> 2x - 7
solve :
x + 2x-7 = 137
To solve this problem, let's assign variables to represent the number of candy bars sold by Maria and Tim.
Let's say Maria sold x candy bars, and Tim sold y candy bars.
According to the information given, we know that Maria sold 7 less than twice the number of candy bars Tim sold. So we can write an equation for Maria's candy bars as:
Maria's candy bars = 2 * Tim's candy bars - 7
We also know that the total number of candy bars sold by Maria and Tim is 137. So we can write another equation:
Maria's candy bars + Tim's candy bars = 137
Now we have a system of two equations:
1) Maria's candy bars = 2 * Tim's candy bars - 7
2) Maria's candy bars + Tim's candy bars = 137
To solve this system of equations, we can substitute equation (1) into equation (2) to eliminate Maria's candy bars:
(2 * Tim's candy bars - 7) + Tim's candy bars = 137
Simplifying the equation, we get:
3 * Tim's candy bars - 7 = 137
Now, we can solve for Tim's candy bars:
3 * Tim's candy bars = 137 + 7
3 * Tim's candy bars = 144
Tim's candy bars = 144 / 3
Tim's candy bars = 48
Now that we know Tim's candy bars, we can substitute this value into equation (1) to find Maria's candy bars:
Maria's candy bars = 2 * 48 - 7
Maria's candy bars = 96 - 7
Maria's candy bars = 89
Therefore, Tim sold 48 candy bars, and Maria sold 89 candy bars.
Let's start by creating some variables to represent the number of candy bars sold by Maria and Tim.
Let's say:
Maria: x candy bars
Tim: y candy bars
According to the given information, Maria sold 7 less than twice the number of candy bars that Tim sold. We can write this as an equation:
Maria's sales: x = 2y - 7 ...(Equation 1)
The total number of candy bars sold by both Maria and Tim is 137, so we have another equation:
Total sales: x + y = 137 ...(Equation 2)
Now we have a system of equations. We can solve this system using substitution or elimination.
Let's use substitution. Rearrange Equation 1 to solve for x:
x = 2y - 7
Substitute this expression for x in Equation 2:
(2y - 7) + y = 137
Combine like terms:
3y - 7 = 137
Add 7 to both sides:
3y = 144
Divide both sides by 3:
y = 48
So, Tim sold 48 candy bars.
Substitute this value back into Equation 1 to find Maria's sales:
x = 2y - 7
x = 2(48) - 7
x = 96 - 7
x = 89
Therefore, Maria sold 89 candy bars.
To summarize:
Maria sold 89 candy bars.
Tim sold 48 candy bars.